An important issue in survival analysis is the investigation and the modeling of hazard rates. Within a Bayesian nonparametric framework, a natural and popular approach is to model hazard rates as kernel mixtures with respect to a completely random measure. In this paper we provide a comprehensive analysis of the asymptotic behaviour of such models. We investigate consistency of the posterior distribution and derive fixed sample size central limit theorems for both linear and quadratic functionals of the posterior hazard rate. The general results are then specialized to various specific kernels and mixing measures yielding consistency under minimal conditions and neat central limit theorems for the distribution of functionals.

Asymptotics for posterior hazards

DE BLASI, Pierpaolo;PRUENSTER, Igor
2009

Abstract

An important issue in survival analysis is the investigation and the modeling of hazard rates. Within a Bayesian nonparametric framework, a natural and popular approach is to model hazard rates as kernel mixtures with respect to a completely random measure. In this paper we provide a comprehensive analysis of the asymptotic behaviour of such models. We investigate consistency of the posterior distribution and derive fixed sample size central limit theorems for both linear and quadratic functionals of the posterior hazard rate. The general results are then specialized to various specific kernels and mixing measures yielding consistency under minimal conditions and neat central limit theorems for the distribution of functionals.
37
1906
1945
http://www.imstat.org/aos/
Asymptotics; Bayesian Consistency; Bayesian Nonparametrics; Central limit theorem; Completely random measure; Path-variance; Random hazard rate; Survival analysis}.
P. De Blasi; G. Peccati; I. Pruenster
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/29154
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